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Special equipment: 13- by 18-inch rimmed baking sheet, parchment paper, stand mixer with whisk attachment or handheld mixer, sifter or sieve, offset spatula, clean cardboard.
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To make the sponge cake: Preheat the oven to 350u00b0F/180u00b0C, and place a rack in the middle of the oven. Line the baking sheet with parchment paper.
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Using the stand mixer or the handheld mixer and a medium bowl, beat together the egg yolks, 1?4 cup (50 g) of the sugar, and the lemon juice on high speed for at least 6 to 8 minutes if using the stand mixer or 10 to 12 minutes if using the handheld mixer, or until thick and doubled in volume. Stop the mixer once or twice and scrape down the sides of the bowl and the whisk to ensure the sugar and yolks are evenly mixed. Transfer to a large bowl and set aside.
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Clean the bowl and the whisk attachment or beaters (they must be spotless) and beat the egg whites on medium speed for 2 to 3 minutes with the stand mixer or 4 to 6 minutes with the handheld mixer, or until soft peaks form. The whites will start to froth and turn into bubbles, and eventually the yellowy viscous part will disappear. Keep beating until you can see the tines of the whisk or beaters leaving a slight trail in the whites. To test for the soft-peak stage, stop the mixer and lift the whisk or beaters out of the whites; the whites should peak and then droop. With the mixer on medium speed, add the remaining 3/4 cup (150 g) sugar very slowly, a spoonful or so at a time, taking about 1 minute to add all of the sugar. Continue beating on medium speed for another 2 to 3 minutes, or until the whites are glossy and shiny and hold a stiff peak when you slowly lift the whisk or beaters straight up and out of the whites.
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Using a rubber spatula, gently fold about one third of the whipped whites into the yolk mixture to lighten it. Then gently fold in the remaining egg whites. Sift the flour and salt together over the top of the mixture and fold in gently until the flour is completely incorporated. Pour the batter into the prepared baking sheet.
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Using the offset spatula, carefully spread the batter evenly to cover the entire baking sheet. Concentrate on spreading the batter toward the corners and edges of the pan. The center will be easier to fill once the edges are filled with batter. Don't worry about the top being perfectly smooth; it is more important that the batter be spread evenly so that the cake is the same thickness throughout. Bake the cake for 18 to 24 minutes, rotating the baking sheet back to front about halfway through, or until the top is pale golden brown and springs back when pressed in the center with your fingertips and the cake doesn't stick to your fingers. Let the cake cool in the pan on the wire rack for about 5 minutes.
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Line a large cutting board with parchment. Run a paring knife around the edge of the still-warm cake to release it from the sides of the baking sheet, and invert the cake onto the parchment. Carefully peel off the parchment and allow the cake to cool completely. Using a chef's knife, cut the cake in half crosswise and then in half lengthwise. You should now have four cake layers, each about 5 1/2 by 8 inches. Cut the cardboard so that its dimensions are just slightly larger than the cake layer dimensions.
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To make the soaking syrup: In a small bowl, stir together the coffee and sugar until the sugar has dissolved.
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Using the pastry brush, brush the top of all four cake rectangles evenly with the soaking syrup, using up all of the syrup.
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Place one cake layer, syrup-side up, on the prepared cardboard rectangle. In a medium bowl, using a mixer or a whisk, whip the heavy cream until it holds very firm, stiff peaks. Fold in the pastry cream (see separate recipe) until well combined. Using the offset spatula, spread about one third of the cream mixture over the cake layer. There is a tendency for the cream to mound in the center, so be sure to spread the cream out to the edges of the cake. In fact, to make the best-looking cake possible, it is better if the cream layer is slightly thicker along the edge than in the center.
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Place a second cake layer, syrup-side up, on top of the cream layer and press down gently so the cake layer is level. Using the offset spatula, spread about half of the remaining cream mixture over the cake layer. Again, you want to spread the cream a bit thicker along the edge of the rectangle to prevent the final cake from doming.
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Place a third cake layer, syrup-side up, on top of the cream and press down slightly to level the cake. Using the offset spatula, spread the remaining cream mixture over the cake, again making it a bit thicker along the edges than in the center. Top the cake with the final cake layer, syrup-side up, and press down gently so that the top layer is flat. Lightly wrap the cake with plastic wrap, place in the freezer, and freeze for about 8 hours or up to overnight, or until it is frozen solid. (At this point, the cake can instead be put into the freezer just until it has firmed up and then it can be well wrapped and frozen for up to 2 weeks.)
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At least 3 hours in advance of serving, remove the cake from the freezer and place it on a cutting board. Using a chef's knife dipped in very hot water, trim the edges of the cake so that they are neat and even. (These trimmings make for great snacking.) Dip and wipe the knife clean several times as you trim to make sure you get a neat, sharp edge on the cake. Trim the cardboard underneath so it is flush with the cake.
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Place the cake on its cardboard base on a cooling rack set on a baking sheet. Pour the warm ganache (see separate recipe) over the top of the cake. Using the offset spatula, spread the ganache in an even layer. It will begin to firm up right away when it hits the cold cake, so work quickly to even the surface. Let the excess ganache drip down the sides of the cake, leaving some parts of the cake exposed. Let the ganache set for several seconds, then transfer the cake to a serving plate. Let the cake thaw at room temperature before serving.
